Question

For what value of x is PQ || BC? A 5 B. 6 C. 7 D. 8

Answer 1

Answer:

C. 7

Step-by-step explanation:

$In\: \triangle ABC\\\overline{PQ} \parallel \overline {BC}.. (given)$

Therefore, by Basic Proportionality theorem:

$\frac{AP}{PB} = \frac{AQ}{QC} \\\\\therefore \frac{x}{x+7} = \frac{x-3}{x+1} \\\\ \therefore \: \frac{x - x - 7}{x + 7} = \frac{x - 3 - x - 1}{x + 1} \\ (by \: dividendo) \\ \\ \frac{ - 7}{x + 7} = \frac{ - 4}{x + 1} \\ \\ \frac{7}{x + 7} = \frac{4}{x + 1} \\ \\ 7x + 7 = 4x + 28 \\ \\ 7x - 4x = 28 - 7 \\ \\ 3x = 21 \\ \\ x = \frac{21}{3} \\ \\ \huge \red{ \boxed{ x = 7}}$